9.1

You can use the following syntax to check your answers. Note the answers you get in R will not be EXACTLY the same you get by hand but they should be pretty close.

If your \(x = 542\) (ie the number of “successes” and your \(n = 3611\), this is how you can have R calculate a 90% Confidence Interval for you.

binom.test(x = 542, n = 3611,  conf.level = .90)[["conf.int"]]
## [1] 0.1403939 0.1602214
## attr(,"conf.level")
## [1] 0.9

25.

  1. .15
  2. Sample is less than 5% of population and 460 > 10.
  3. .1402, .1598
  4. I am 90% confident that the proportion is between .1402 and .1598.

26.

  1. .43
  2. Sample is less than 5% of population and 282.6 > 10.
  3. .4014, .4585
  4. I am 95% confident that the proportion is between .4014 and .4585.

27.

  1. .519
  2. Sample is less than 5% of population and 282.6 > 10.
  3. .488, .550
  4. It is possible but not likely.
  5. .45, .512

28.

  1. .75
  2. Sample is less than 5% of population and 192 > 10.
  3. .715, .785
  4. It is possible but not likely
  5. .215, .285

29.

  1. .54
  2. Sample is less than 5% of population and 434.2 > 10.
  3. .52, .56
  4. .509, 571
  5. Increasing the level of confidence increases the width of the interval.

9.2

You can use the following syntax to check your answers. Note the answers you get in R will not be EXACTLY the same you get by hand but they should be pretty close.

If \(\bar{x} = 18.4\), sample standard deviation is 4.5, sample size = 35, and your confidence level is 95% this is how you can have R calculate a Confidence Interval for you.

conf_int(xbar = 18.4, size = 35, conf = .95, s = 4.5)
## [1] 16.8542 19.9458

21.

  1. 16.854, 19.945
  2. 17.2, 19.68
  3. 16.32, 20.48
  4. The population must be normal if n<30

23.

  1. False, 95% is the confidence interval not the probability
  2. True
  3. False, 95% is the confidence interval not the population
  4. False, 95% is the confidence interval for all of America not just specifically Idaho.

25.

We are 90% confident that the mean drive thru serice time of Taco Bell is between 161.5 seconds and 164.7 seconds

27.

Increase the random sample size to decrease the margin of error. Decrease the confidence interval to decrease the margin of error.

29.

  1. Because it is skewed right, the sample must be large so that the distribution of the sample mean will be normal.
  2. n=51, N=25000 -> sample size is less than 5% of the population
  3. .164, .169
  4. It is possible, though unlikely, that the true mean is not within the confidence interval

31.

12.05, 14.75

33.

1.08, 8.11

9.3

You can use the following syntax to check your answers. Note the answers you get in R will not be EXACTLY the same you get by hand but they should be pretty close.

If you sample standard deviation s = 2, the sample size = 35, and your confidence level is 95% this is how you can have R calculate a Confidence Interval for \(\sigma\).

conf_sig(s = 2, size = 35, conf = .95)
## [1] 1.617744 2.620404

5

α/2: 30.144 1-α/2: 10.117

7

α/2: 40.289 1-α/2: 9.542

9

  1. 7.94, 23.66
  2. 8.58, 20.63 -increasing the sample size decreased the interval size
  3. 6.61, 31.36 -increasing the confidence level increased the interval size

11

1.612, 4.278

13

849.693, 1655.34